I personally tend to play one single game at time and play it until I get completely bored of it. Experimenting different things, trying to understand it's story and mechanics well, discovering things I had not in previous playthroughs, and so on.
The good about this is that you understand all its mechanics and story with full focus on it, the bad is that when you get bored of, you really do tire of that game for a while - sometimes a long while.
Depending on the game, though, I play two at time, to avoid fatigue. Like others said here a "story focused" game, with a "mechanics focused" game.
I think I've always been like this too, specially with console games in the past, which I remember playing only one game at time ad nauseam, in all it's difficulties, getting secrets, speed running levels... Nowdays I'm not so patient to do this anymore, but I still focus on one game at time more.